SMITH, BENJAMIN CHRISTIAN. Modeling the Diameter Distribution in Juvenile Loblolly
Pine (Pinus taeda L.) from Diverse Genetic Provenances Under Deficient and Optimum
Nutrition Regimes. (Under the direction of Dr. Bronson P. Bullock.)
The ability to predict diameter distributions is an important tool for the forest
manager; by accurately predicting the diameter distribution, the manager may make betterinformed
decisions regarding the silvicultural treatments for a stand. This study compares
the suitability of the gamma, lognormal, and two-parameter Weibull distributions for
modeling diameter distributions in juvenile loblolly pine from ages 5 to 11. The twoparameter
Weibull distribution was found to be the most appropriate distribution as
determined by the Anderson-Darling goodness-of-fit statistic. The study also determined the
most suitable method for estimating distributional parameters from stand level characteristics
(e.g. mean basal area, relative spacing, quadratic mean diameter, and age). Methods tested
were a parameter prediction method (PPM), a parameter recovery method (PRM), and a
percentiles-based method (PCT). Comparisons were made from ages 5 to 10 using a
modification of the Reynolds error index, weighted by basal area. Final parameter estimation
equations were developed for juvenile loblolly pine over ages 5 to 11.
The parameter recovery method of parameter estimation proved to be most
appropriate for modeling these data. Although the PPM had a slightly lower Reynolds error
index than the PRM, the shape parameter was predicted within a very narrow range about the
mean, while the distribution of shape parameters recovered by the PRM was much closer to
the empirical distribution. In addition, the PRM required fewer inputs into the model, and as
such was more desirable for modeling purposes. An application of the PRM was presented
to demonstrate the construction of stand tables from the estimated parameters.
The relationships among the maximum likelihood fitted parameters of the twoparameter
Weibull distribution and the treatment effects due to fertilization, genetic
provenances, and open-pollinated genetic families were also examined. Both the scale and
shape parameters differed significantly between the non-fertilized control treatment and the
optimally fertilized treatment. No significant differences were observed in the shape
parameters between genetic provenances, but significant differences did exist in the younger
ages between provenances in the scale parameters.
Family means tended to increase over time for the scale parameter, and family mean
rankings were relatively stable within and across fertilization treatments. The shape
parameter family mean rankings were less stable over time than the scale parameter ranks,
with the means tending to increase in the non-fertilized treatment and decrease in the
fertilized treatment, reflecting the differences in stand development. Year to year rank
changes were more minor than long-term family mean rankings.
Modeling the Diameter Distribution in Juvenile Loblolly Pine (Pinus taeda L.) from Diverse
Genetic Provenances Under Deficient and Optimum Nutrition Regimes
by
Benjamin Christian Smith
A thesis submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the Degree of
Master of Science
Forestry
Raleigh, North Carolina
2007